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Propositional Logic Worksheet Extraction

Total questions: 84

Worksheet time: 4hrs 5mins

Name
Class
Date
1.

Explain the meaning of a premise, used in an argument. Provide an example of a valid argument. Label the premises and provide a true conclusion.

4 lines
2.

Define simple and compound statements in propositional logic.

4 lines
3.

Define conjunction in propositional logic and give its symbol.

4 lines
4.

Define disjunction in propositional logic and give its symbol.

4 lines
5.

Define conditional and biconditional statements, and discuss different ways to express them.

4 lines
6.

Discuss the use of existential and universal quantifiers.

4 lines
7.

Discuss the use of truth tables in propositional logic.

4 lines
8.

Use a truth table to validate the rule of detachment. Explain how the truth table validates the rule.

4 lines
9.

Use a truth table to validate the chain rule. Explain how the truth table validates the rule.

4 lines
10.

Consider the premises below: If I hike a mountain, I will not eat a sandwich. If I do not eat a sandwich, I will drink some water. I will not drink some water. Write a valid conclusive statement. Explain how you arrived at your answer. Be specific in your explanation.

4 lines
11.

Define the converse, inverse, and contrapositive of a conditional statement.

4 lines
12.

Define negation in propositional logic, and give its symbol.

4 lines
13.

State De Morgan’s laws, and explain how to prove their validity.

4 lines
14.

Explain the meaning of inductive reasoning. Provide a couple of examples, one mathematical and one non-mathematical.

4 lines
15.

Explain the meaning of deductive reasoning. Provide an example. Explain why the example shows deductive reasoning.

4 lines
16.

Define formal reasoning. Provide an example, whereby formal reasoning is used to justify some mathematical idea.

4 lines
17.

Define informal reasoning. Provide an example whereby informal reasoning is used to justify some mathematical idea.

4 lines
18.

Discuss the purpose of a proof.

4 lines
19.

Define direct proofs. Provide a sample proof.

4 lines
20.

Define indirect proofs. Provide a sample proof.

4 lines
21.

Define and contrast proofs by contraposition and contradiction. Provide a sample proof for contraposition.

4 lines
22.

Explain how, and where, a mathematical induction proof utilizes inductive reasoning. Provide an excerpt of a proof, to support your explanation.

4 lines
23.

Define the following common arithmetic terms specific to numbers: integers, prime, composite, even, and odd.

4 lines
24.

Explain the decimal system and define the terms decimal, decimal point, and decimal place.

4 lines
25.

Describe rational, irrational, and real numbers.

4 lines
26.

Which word form correctly represents the number 4,546.09 using place value?

a)

four thousand five hundred forty-six and nine hundredths

b)

four thousand five hundred sixty-four and nine tenths

c)

four thousand fifty-four and six hundred nine thousandths

d)

four thousand five hundred forty-six and ninety hundredths

27.

Define rational and irrational numbers.

4 lines
28.

Describe number lines and their use.

4 lines
29.

On a number line marked at 0, 1, 2, and 3, four points are labeled A, B, C, and D from left to right over the tick marks. Which complete mapping of labels to values is correct?

a)

A=0, B=1, C=2, D=3

b)

A=1, B=0, C=2, D=3

c)

A=0, B=2, C=1, D=3

d)

A=3, B=2, C=1, D=0

30.

Which statement correctly defines absolute value and explains why 3=∣−3∣3 = \lvert -3 \rvert using a number line?

a)

Absolute value is the distance from zero; both 3 and −3 are three units from 0, so their absolute values are 3.

b)

Absolute value is the largest number on the line; since 3 is larger than −3, ∣−3∣=3\lvert -3 \rvert = 3 by comparison.

c)

Absolute value changes negative numbers to zero; therefore ∣−3∣=0\lvert -3 \rvert = 0 and 3 equals 0.

d)

Absolute value is the sign of a number; positive numbers have absolute value 1 and negatives have absolute value −1.

31.

Define mathematical expressions and operations.

4 lines
32.

List the basic mathematical operations of addition and subtraction and give examples of each.

4 lines
33.

List the basic mathematical operations of multiplication and division and give examples of each.

4 lines
34.

Describe parentheses and exponents.

4 lines
35.

Discuss roots and explain how they relate to exponents.

4 lines
36.

Demonstrate how to translate common mathematical verbal phrases into mathematical phrases.

4 lines
37.

Discuss subtraction with regrouping.

4 lines
38.

Demonstrate how to subtract 189 from 525 using regrouping.

4 lines
39.

Explain the correct order of operations, including a discussion of PEMDAS.

4 lines
40.

Outline the properties of exponents.

4 lines
41.

Define the term factor and explain common and prime factors with examples.

4 lines
42.

Define greatest common factor (GCF) and least common multiple (LCM).

4 lines
43.

Explain fractions, numerators, and denominators.

4 lines
44.

Discuss improper fractions and mixed numbers.

4 lines
45.

Describe the process for adding, subtracting, multiplying, and dividing fractions.

4 lines
46.

Discuss the process of multiplying a mixed number by another number and work through an example.

4 lines
47.

Explain how to compare fractions using a common denominator.

4 lines
48.

Explain how to compare fractions using decimals.

4 lines
49.

Explain how to compare fractions using cross-multiplication.

4 lines
50.

Describe decimals and their relationship to powers of ten and fractions.

4 lines
51.

Describe the process of adding and subtracting decimals.

4 lines
52.

Describe how to multiply using decimals.

4 lines
53.

Explain the process of dividing with decimals.

4 lines
54.

Explain the relationships between percentages, fractions, and decimals.

4 lines
55.

Discuss percentage problems and the process to be used for solving them.

4 lines
56.

Explain the process of converting between percentages, decimals, and fractions.

4 lines
57.

Define proportion and give examples.

4 lines
58.

Define ratio and give examples.

4 lines
59.

Define constant of proportionality.

4 lines
60.

Describe and discuss unit rate.

4 lines
61.

Discuss mathematical expressions.

4 lines
62.

Define single variable and general linear expressions.

4 lines
63.

Demonstrate the use of a unit rate as the slope.

4 lines
64.

Discuss linear equations and define the following associated terms: solution set, empty set, equivalent equations, and identity.

4 lines
65.

Outline the different forms for linear equations.

4 lines
66.

Explain how to solve one-variable linear equations.

4 lines
67.

Kim’s savings are represented by the table below. Represent her savings, using an equation. Explain how the equation was found.

4 lines
68.

Define like terms in an equation, and give examples.

4 lines
69.

Explain why the same operation must always be carried out on both sides of an equation.

4 lines
70.

Explain the advantage of combining like terms, and give an example of doing so.

4 lines
71.

Identify the circumstances in which you can cancel terms on opposite sides of an equation.

4 lines
72.

Define what it means to isolate a variable, and describe how it can be accomplished.

4 lines
73.

Explain the circumstances where an equation may have more than one solution, and give examples.

4 lines
74.

Explain the circumstances where an equation may have no solution, and give examples.

4 lines
75.

Define a linear equation, and give some examples of equations that are not linear.

4 lines
76.

Explain how to solve an equation that involves roots, such as 2x+1−1=32\sqrt{x} + 1 - 1 = 3 .

4 lines
77.

Explain how to solve an equation with an exponent such as 2x3+17=5x3−72x^3 + 17 = 5x^3 - 7 or (x−1)2−1=3(x - 1)^2 - 1 = 3 .

4 lines
78.

Explain how to solve an equation with an absolute value, such as ∣2x−1∣+x=5|2x - 1| + x = 5 .

4 lines
79.

Define a spurious solution and explain how it can be identified.

4 lines
80.

Explain how to choose which variable to isolate in a two-variable equation.

4 lines
81.

Discuss how to find an unknown in equivalent expressions.

4 lines
82.

Explain graphing and the Cartesian coordinate plane.

4 lines
83.

Explain how to graph an equation in two variables such as y=2x−1y = 2x - 1 .

4 lines
84.

Discuss inequalities, including conditional, absolute, and double inequalities.

4 lines

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